RESP M is calculated as a function of temperature and biomass, and it is subtracted directly from the pool of assimilates. Whenever maintenance respiration exceeds the pool of assimilates, the deficit is discounted from the reserve pool. The remaining assimilates are distributed among the different organs with partitioning rules being mediated by phenology. The loss of carbon during the synthesis of new biomass was included by calculating a production value ( PV) ( Penning de Vries et al., 1974) for each type of organ according to its biochemical composition.

De Melo-Abreu, J. P., Barranco, D., Cordeiro, A. M., Tous, J., Rogado, B. M., and Villalobos, F. J. (2004). Modelling olive flowering date using chilling for dormancy release and thermal time. Agric. For. Meteorol. 125, 117–127. doi: 10.1016/j.agrformet.2004.02.009 Mariscal, M. J., Orgaz, F., and Villalobos, F. J. (2000). Radiation-use efficiency and dry matter partitioning of a young olive ( Olea europaea) orchard. Tree Physiol. 20, 65–72. doi: 10.1093/treephys/20.1.65 Citation: López-Bernal Á, Morales A, García-Tejera O, Testi L, Orgaz F, De Melo-Abreu JP and Villalobos FJ (2018) OliveCan: A Process-Based Model of Development, Growth and Yield of Olive Orchards. Front. Plant Sci. 9:632. doi: 10.3389/fpls.2018.00632 When available, the values of the different parameters were taken from the literature. Supplementary Table S2 provides a complete list with the parameter values used for the simulations and the source from which they were taken. In short, the parameters of the SPAC model were taken from García-Tejera et al. (2017a, b), who, in turn, gathered most of the parameter values from different sources. Parameters related to phenology were obtained from reports by De Melo-Abreu et al. (2004) and López-Bernal et al. (2014, 2017). The studies by Mariscal et al. (2000) and Pérez-Priego et al. (2014) were used for setting the maintenance respiration and PV coefficients, respectively. Parameters related to the calculation of fruit number and yield were taken from several sources, including experimental data (see section “Number of Fruits and Alternate Bearing” in Supplementary Material). The coefficient of oil yield to dry fruit matter was taken from experimental data collected in a hedgerow cv. ‘Arbequina’ orchard ( López-Bernal et al., 2015). Partitioning coefficients were based on findings by Mariscal et al. (2000); Villalobos et al. (2006) and Scariano et al. (2008). Reports from Barranco et al. (2005) and Koubouris et al. (2009) were used to parametrize the routines modeling the impacts of frost damage and heat stress, respectively. Coefficients modulating fine root growth distribution were directly taken from Jones and Kiniry (1986). Finally, parameters implied in the soil carbon balance were taken from Verstraeten et al. (2006); Huang et al. (2009) and, to a lesser extent, from other studies. Model Testing

The research leading to these results has received funding from Ministerio de Economía y Competitividad (Grant Nos. AGL-2010-20766 and AGL2015-69822), from Junta de Andalucía (Grant No. P08-AGR-04202), from the European Community’s Seven Framework Programme-FP7 (KBBE.2013.1.4-09) under Grant Agreement No. 613817. 2013–2016 “MODelling vegetation response to EXTREMe Events” (MODEXTREME, modextreme.org) and from ERA-NET FACCE SURPLUS (Grant No. 652615, project OLIVE-MIRACLE), the latter co-funded by INIA (PCIN-2015-259). Besides, ÁL-B was funded by a postdoctoral fellowship (‘Juan de la Cierva-Formación 2015’ Programme, FJCI-2015-24109) from Ministerio de Economía y Competitividad. Conflict of Interest Statement Testi, L., Villalobos, F. J., Orgaz, F., and Fereres, E. (2006). Water requirements of olive orchards: I simulation of daily evapotranspiration for scenario analysis. Irrig. Sci. 24, 69–76. doi: 10.1007/s00271-005-0011-y During the vegetative rest period and provided that fruits are not present, all the available assimilates after discounting maintenance respiration are allocated to a virtual pool of reserves. Such reserve pool is subsequently used for the growth of vegetative organs and fruits during the growth season. Fruit growth can either be source-limited or sink-limited. In the former case, the associated partitioning coefficient is fixed whereas in the latter, it is calculated as a function of the number of fruits ( FN), which in turn is modeled as a function of the number of fruits and nodes produced in the previous year. In doing so, the model may be prone to errors in the estimates of productivity and vegetative growth for a given year when performing long runs, but such errors are to be compensated if those model outputs are averaged over biennia. With regard to the vegetative organs, fixed partitioning coefficients are adopted. Whenever fruits are present, the model considers that they become the prioritary sink of assimilates, thus the vegetative partitioning coefficients are applied after discounting the fruit demand from the daily pool of assimilates. Therefore, partitioning coefficients to vegetative organs are assumed to be independent of tree size, management factors and environmental conditions, as in the model of Morales et al. (2016). As a final remark, inspired by the CERES-type models ( Jones and Kiniry, 1986), the growth of fine roots is distributed among the different layers in the two soil zones as a function of the size and water content of each soil compartment. Iniesta, F., Testi, L., Orgaz, F., and Villalobos, F. J. (2009). The effects of regulated and continuous deficit irrigation on the water use, growth and yield of olive trees. Eur. J. Agron. 30, 258–265. doi: 10.1016/j.eja.2008.12.004

Considering its mechanistic approach, the vast quantity of simulated processes and its potential uses, OliveCan represents a momentous step forward in relation to previous olive growth simulation models. In this regard, OliveCan enables one to assess the combined effects of management operations and weather over crop performance for different olive orchard and soil typologies both under unstressed and water deficit conditions. Thus, the model shows potential for a broad range of research applications. For instance, OliveCan seems particularly suitable for assessing the performance of olive orchards under future climatic scenarios, as the model explicitly accounts for the multiple effects of reduced rainfall and increased environmental CO 2 and temperature for the water and carbon balances of the orchard and the development of trees.Pastor, M., García-Vila, M., Soriano, M. A., Vega, V., and Fereres, E. (2007). Productivity of olive orchards in response to tree density. J. Hortic. Sci. Biotechnol. 82, 555–562. doi: 10.3389/fpls.2017.01280 Finally, future improvements of OliveCan might include additional sub-models for simulating nutrient uptake and the impact of pests and diseases. Apart from that, the model shows potential for being adapted to other tree species, so its interest may not be only restricted to olive researchers. Conclusion OliveCan is subdivided into three main components (Supplementary Figure S1) that are devoted to the computation of the water and carbon balances of the olive orchard and to simulate the impacts of some management operations. The water and carbon balance components are interdependent (i.e., each one needs data provided by the other) and both of them require information on soil traits and weather data. Simulating the water balance of an irrigated olive orchard is a particularly challenging task as the trees are typically watered by point-source emitters that keep a small fraction of the surface frequently wet while the remaining area remains dry, unless it rains. This fact results in differences between these two soil areas in relation to soil water content, the water fluxes determining the water balance (i.e., runoff, drainage, redistribution along the soil profile, soil evaporation, and root water uptake) and root length density ( Fernández et al., 1991). Therefore, traditional modeling approaches based on the use of the average soil water content can lead to large errors, besides giving a poor insight into the system. One alternative consists of using a two-compartment model that solves the water balance separately for each zone of the soil. In this regard, Testi et al. (2006) proposed a model capable of simulating potential transpiration, separately calculating runoff, drainage and soil evaporation from the wet and dry fractions of the soil surface under localized irrigation. The model was developed to determine the potential irrigation needs of olive orchards, so its use is unfortunately limited to unstressed conditions. Lately, García-Tejera et al. (2017a) have formulated a soil-plant-atmosphere-continuum (SPAC) model capable of calculating root water uptake from soils with spatially heterogeneous distributions of water content and root length densities. Such a model also discretizes the soil into different soil zones and layers and, for the canopy, it considers two leaf classes (i.e., sunlit and shaded). Furthermore, the model by García-Tejera et al. (2017a) provides estimates of gross assimilation ( A), offering an opportunity to link the water and carbon balances of olive trees. Gardner, W. R. (1960). Dynamic aspects of water availability to plants. Soil Sci. 89, 63–73. doi: 10.1097/00010694-196002000-00001

Experimental measurements conducted in two mature olive orchards located in the Alameda del Obispo Research Station, Córdoba, Spain (37.8°N, 4.8°W, 110 m) were used for assessing the reliability of OliveCan. The climate in the area is typically Mediterranean, with around 600 mm of average annual rainfall and 1390 mm and average annual ET 0 of 1390 mm ( Testi et al., 2004), respectively. The soil for both orchards is classified as a Typic Xerofluvent of sandy loam texture and exceeds 2 m in depth, with field capacity (𝜃 UL) and permanent wilting point (𝜃 LL) water contents of 0.23 m 3 m -3 and 0.07 m 3 m -3, respectively ( Testi et al., 2004). Weather data were collected using a station placed 500 m away from the orchards. Within both orchards, irrigation experiments comprising several irrigation treatments were performed. Each irrigation treatment was simulated separately with OliveCan. Experiment I Two phenological stages are considered for the vegetative organs: (i) a dormant stage characterized by an absence of growth that is induced by chilling accumulation during autumn and (ii) a phase of active growth that starts in late winter, by the time average temperature is above a threshold. In relation to the reproductive growth, the date of flowering is determined with the two-phase model by De Melo-Abreu et al. (2004). Fruit growth is assumed to start after a given amount of thermal time is accumulated from the date of flowering and ceases when either maturity or the harvest date is reached. Keep in a cool and dry place, away from direct sunlight. Once opened, keep refrigerated covered in the brine and consume within 7 days. Values of GC, LAD, and R zx required to initialize the model were taken from measurements of tree silhouettes. A record of Y dry of the year preceding simulations was also considered. Initial L v values were taken from records measured by Moriana (2001) for the trees of Experiment II. Experiment II Overall, the results of all the aforementioned comparisons suggest that model performance is fairly satisfactory. However, further testing against experimental data taken from different environmental conditions and orchard characteristics seems highly desirable. This would help to provide additional evidence on the predictive power of OliveCan, or else to identify situations for which model accuracy could be improved through either better calibrations or reformulation of some routines. Apart from that, it should be noted that the reliability of OliveCan for estimating certain output parameters (e.g., NEE, RESP H) has not been tested specifically in the present study, which should also be the focus of future research efforts. Model ApplicabilityHuang, Y., Yu, Y., Zhang, W., Sun, W., Liu, S., Jiang, J., et al. (2009). Agro-C: a biogeophysical model for simulating the carbon budget of agroecosystems. Agric. For. Meteorol. 95, 203–223. doi: 10.1016/j.agrformet.2008.07.013 Where M i is the ith measured variable, M ¯ is the average value of all measurements, S i is the ith simulated variable and n is the number of measured values. In addition, the slope, intercept and coefficient of determination ( r 2) obtained by regressing the simulated and measured values were also used. Results Bustan, A., Avni, A., Lavee, S., Zipori, I., Yeselson, Y., Schaffer, A., et al. (2011). Role of carbohydrate reserves in yield production of intensively cultivated oil olive ( Olea europaea L.) trees. Tree Physiol. 31, 519–530. doi: 10.1093/treephys/tpr036 Morales, A., Leffelaar, P. A., Testi, L., Orgaz, F., and Villalobos, F. J. (2016). A dynamic model of potential growth of olive ( Olea europaea L.). Eur. J. Agron. 74, 93–102. doi: 10.1016/j.eja.2015.12.006

Want more olive appetizers? Try my Olive Dip and Olive Cheese Ball! What to Serve with Blue Cheese Stuffed OlivesVialet-Chabrand, S., Dreyer, E., and Brendel, O. (2013). Performance of a new dynamic model for predicting diurnal time courses of stomatal conductance at the leaf level. Plant Cell Environ. 36, 1529–1546. doi: 10.1111/pce.12086 Scariano, L., Lo Bianco, R., Di Marco, L., and Policarpo, M. (2008). “Dynamics of dry matter partitioning in young ‘Nocellara del Belice’ olive trees,” in Proceedings of the Fifth International Symposium on Olive Growing, Vols 1 and 2, ed. M. T. L. S. F. L. Ozkaya (Leuven: Acta Horticulturae), 397–401. doi: 10.17660/ActaHortic.2008.791.58 Control irrigation (CON), which applied the required water to match the maximum ET, discounting rainfall. The maximum ET was estimated using the model of Orgaz et al. (2006).